Sliding-mode set-valued control and observation in finite and infinite dimensions: discretization – SLIMDISC

The objectives of this project are focused on the analysis and experimental validation of multivalued control laws and observers/differentiators based on the theory of sliding mode, in discrete time, mainly using implicit and semi-implicit Euler algorithms. Indeed, it has been recognized for some years that time discretization has a considerable influence on the behavior and properties of multivalued sliding-mode control laws and observers which has been widely experimentally verified (by the consortium of this project, and by groups in Japan, Mexico, Austria, China).
More precisely, the project is divided into three parts: the first part is theoretical, and will be devoted to the study of implicit discrete-time sliding mode control for PDE-type systems on the one hand, and the study of discrete-time multivalued control by output feedback on the other one.
The second part of the project aims to experimentally validate the concepts developed in the first part of the project on 2 different systems, which are complementary in terms of their modeling (non-linear ODEs, PDEs): in this way, the project will offer the possibility of studying the control of a cable driven robot, and the control of an aerodynamic flow. Finally, a third part aims to develop a toolbox for calculating control laws in discrete time using the implicit method.